By the end of this lesson, you should be able to:
- Recognise a number written in standard form.
- Convert large numbers into standard form.
- Convert small numbers into standard form.
- Change a number from standard form back to an ordinary number.
What Is Standard Form?
Standard form is a way of writing very large or very small numbers in a compact form. A number in standard form is written as:
where 1 ≤ a < 10 and n is an integer.
The first number, a, must be at least 1 but less than 10. The power of 10 tells us how far the decimal point has moved.
Large Numbers
To write a large number in standard form, move the decimal point until the first part is between 1 and 10.
Write 4,500,000 in standard form.
- Move the decimal point after the first non-zero digit: 4.5.
- Count the number of places the decimal point moved: 6.
- Because the original number is large, use a positive power.
Write 72,000 in standard form.
Move the decimal point five places to the left.
Small Numbers
For a number between 0 and 1, move the decimal point to the right until the first part is between 1 and 10.
Write 0.00056 in standard form.
- Move the decimal point to make 5.6.
- Count the places moved: 4.
- Because the original number is small, use a negative power.
Changing Standard Form Back to an Ordinary Number
The sign of the power tells you which direction to move the decimal point. A positive power moves it to the right; a negative power moves it to the left.
Move the decimal point 5 places to the right.
320,000Move the decimal point 3 places to the left.
0.0064Common Mistakes to Avoid
In standard form, the first number must be at least 1 but less than 10.
Large numbers use positive powers; numbers between 0 and 1 use negative powers.
Count every decimal-place movement carefully before writing the power of 10.
Quick Practice
Try these questions without looking at the answers first.